# Improper Integral Convergence

1. Feb 19, 2009

### aostraff

1. The problem statement, all variables and given/known data
I'm trying to show that this improper integral converges
$$\int_{0}^{1} \sin \left ( x + \frac{1}{x} \right )dx$$

2. Relevant equations

3. The attempt at a solution
I thought a comparison test would be nice but I can't think of the right one if that is the way to go. I don't think a substitution of u = x + 1/x works too well as well.

Thanks.

2. Feb 19, 2009

### Staff: Mentor

-1 <= sin(x + 1/x) <= 1

3. Feb 19, 2009

### aostraff

I see. Thanks.